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Steven Robert Mcdougall - One of the best experts on this subject based on the ideXlab platform.
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the extended Washburn Equation and its application to the oil water pore doublet problem
Journal of Colloid and Interface Science, 1995Co-Authors: Kenneth Stuart Sorbie, Steven Robert McdougallAbstract:Abstract The Equations of capillary rise or wetting-phase imbibition into a cylindrical capillary are frequently described by the Washburn Equation. From this starting point, the familiar pore doublet model for imbibition into a wide/narrow pair of pores has been developed. This simple analytically soluble model can afford insights into the physics of immiscible water/oil displacements in porous media, which are of importance to waterflooding of oil reservoirs. Here, we reexamine the basis of both the Washburn Equation and the formulation of the pore doublet model by incorporating a more rigorous treatment of the fluid mechanics. We have extended Equations previously proposed by Szekely et al. to describe water/off displacement in a capillary and it transpires that certain additional inertial terms, which appear in the full formulation of the capillary displacement problem, may be particularly important at the pore size and aspect ratio commonly encountered within porous media. The main result of this additional physics is that the pore filling time and the relative filling order of large and small pores may change since these quantities depend on the pore aspect ratio in the extended formulation. When this fuller formulation is embedded within the extended pore doublet model, we find that the modified Equations lead to different findings for certain cases, compared with previous well-known (analytical) solutions. The original pore doublet model is fully characterised by three quantities, the aspect ratio, r 2 / L , the ratio of capillary radii, r 1 / r 2 , and the fluid "supply," i.e., free supply or restricted supply, which is characterized by a velocity, V 0 2 . In the extended pore doublet model there is a fourth governing quantity, the pore scale Reynolds number, N Re , which describes the inertial terms in the extended Washburn Equation. The resulting coupled differential Equations for the extended pore doublet model do not admit an analytical solution and must be solved numerically. Under certain conditions of very restricted supply of wetting fluid (low V 0 2 ), the extended model agrees very closely with the conventional pore doublet results. However, there are cases which are common at the pore scale (and pore aspect ratio) where significant differences are seen. The relevance of these findings to the modeling of imbibition processes within network models of porous media is discussed.
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The Extended Washburn Equation and Its Application to the Oil/Water Pore Doublet Problem
Journal of Colloid and Interface Science, 1995Co-Authors: Kenneth Stuart Sorbie, Steven Robert McdougallAbstract:Abstract The Equations of capillary rise or wetting-phase imbibition into a cylindrical capillary are frequently described by the Washburn Equation. From this starting point, the familiar pore doublet model for imbibition into a wide/narrow pair of pores has been developed. This simple analytically soluble model can afford insights into the physics of immiscible water/oil displacements in porous media, which are of importance to waterflooding of oil reservoirs. Here, we reexamine the basis of both the Washburn Equation and the formulation of the pore doublet model by incorporating a more rigorous treatment of the fluid mechanics. We have extended Equations previously proposed by Szekely et al. to describe water/off displacement in a capillary and it transpires that certain additional inertial terms, which appear in the full formulation of the capillary displacement problem, may be particularly important at the pore size and aspect ratio commonly encountered within porous media. The main result of this additional physics is that the pore filling time and the relative filling order of large and small pores may change since these quantities depend on the pore aspect ratio in the extended formulation. When this fuller formulation is embedded within the extended pore doublet model, we find that the modified Equations lead to different findings for certain cases, compared with previous well-known (analytical) solutions. The original pore doublet model is fully characterised by three quantities, the aspect ratio, r 2 / L , the ratio of capillary radii, r 1 / r 2 , and the fluid "supply," i.e., free supply or restricted supply, which is characterized by a velocity, V 0 2 . In the extended pore doublet model there is a fourth governing quantity, the pore scale Reynolds number, N Re , which describes the inertial terms in the extended Washburn Equation. The resulting coupled differential Equations for the extended pore doublet model do not admit an analytical solution and must be solved numerically. Under certain conditions of very restricted supply of wetting fluid (low V 0 2 ), the extended model agrees very closely with the conventional pore doublet results. However, there are cases which are common at the pore scale (and pore aspect ratio) where significant differences are seen. The relevance of these findings to the modeling of imbibition processes within network models of porous media is discussed.
Krishna M. Pillai - One of the best experts on this subject based on the ideXlab platform.
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darcy s law based numerical simulation for modeling 3d liquid absorption into porous wicks
Aiche Journal, 2011Co-Authors: Reza Masoodi, Hua Tan, Krishna M. PillaiAbstract:Liquid imbibition into polymer wicks, where a clear liquid front can be seen rising during the wicking process, is modeled using the concepts of flow in porous media. The flow of liquid behind the moving liquid front is modeled using the physics of single-phase flow in a porous medium where the Darcy’s law is combined with the continuity Equation and a capillary suction pressure is imposed at the liquid front. A novel numerical simulation PORE-FLOW V C based on the finite element/control volume method is proposed to model such imbibitional flows in wicks of complex shapes. A validation of the simulation is obtained by achieving an excellent comparison of its predictions with an experimental result, an analytical solution, and the Washburn Equation for the case of wicking against gravity in a cylindrical wick. The simulation is also used to predict a case of two-dimensional (2D) wicking in the altered cylindrical wicks with two different cross-sectional areas. Once again an excellent match is obtained with the experimental results, while analytical solutions for the single and double cross-section cases along with the Washburn Equation fail to predict the 2D wicking. Later, some other types of altered wicks with sharp changes in their cross-sectional areas were analyzed numerically for their wicking behavior. It was observed that the height of liquid front in a vertical wick as a function of time, which is proportional to the history of liquid imbibed, is strongly dependent on the extent of reduction in the wick cross-sectional area as well as its location vis-a `-vis the wick entrance. V C 2010 American Institute of Chemical Engineers AIChE J, 57: 1132–1143, 2011
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darcy s law based model for wicking in paper like swelling porous media
Aiche Journal, 2010Co-Authors: Reza Masoodi, Krishna M. PillaiAbstract:The wicking of liquid into a paper-like swelling porous medium made from cellulose and superabsorbent fibers was modeled using Darcy's law. The work is built on a previous study in which the Washburn Equation, modified to account for swelling, was used to predict wicking in a composite of cellulose and superabsorbent fibers. In a new wicking model proposed here, Darcy's law for flow in porous media is coupled with the mass conservation Equation containing an added sink or source term to account for matrix swelling and liquid absorption. The wicking-rate predicted by the new model compares well with the previous experimental data, as well as the modified Washburn Equation predictions. The effectiveness of various permeability models used with the new wicking model is also investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2010
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Darcy's law–based numerical simulation for modeling 3D liquid absorption into porous wicks
AIChE Journal, 2010Co-Authors: Reza Masoodi, Hua Tan, Krishna M. PillaiAbstract:Liquid imbibition into polymer wicks, where a clear liquid front can be seen rising during the wicking process, is modeled using the concepts of flow in porous media. The flow of liquid behind the moving liquid front is modeled using the physics of single-phase flow in a porous medium where the Darcy’s law is combined with the continuity Equation and a capillary suction pressure is imposed at the liquid front. A novel numerical simulation PORE-FLOW V C based on the finite element/control volume method is proposed to model such imbibitional flows in wicks of complex shapes. A validation of the simulation is obtained by achieving an excellent comparison of its predictions with an experimental result, an analytical solution, and the Washburn Equation for the case of wicking against gravity in a cylindrical wick. The simulation is also used to predict a case of two-dimensional (2D) wicking in the altered cylindrical wicks with two different cross-sectional areas. Once again an excellent match is obtained with the experimental results, while analytical solutions for the single and double cross-section cases along with the Washburn Equation fail to predict the 2D wicking. Later, some other types of altered wicks with sharp changes in their cross-sectional areas were analyzed numerically for their wicking behavior. It was observed that the height of liquid front in a vertical wick as a function of time, which is proportional to the history of liquid imbibed, is strongly dependent on the extent of reduction in the wick cross-sectional area as well as its location vis-a `-vis the wick entrance. V C 2010 American Institute of Chemical Engineers AIChE J, 57: 1132–1143, 2011
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Darcy's law‐based model for wicking in paper‐like swelling porous media
Aiche Journal, 2010Co-Authors: Reza Masoodi, Krishna M. PillaiAbstract:The wicking of liquid into a paper-like swelling porous medium made from cellulose and superabsorbent fibers was modeled using Darcy's law. The work is built on a previous study in which the Washburn Equation, modified to account for swelling, was used to predict wicking in a composite of cellulose and superabsorbent fibers. In a new wicking model proposed here, Darcy's law for flow in porous media is coupled with the mass conservation Equation containing an added sink or source term to account for matrix swelling and liquid absorption. The wicking-rate predicted by the new model compares well with the previous experimental data, as well as the modified Washburn Equation predictions. The effectiveness of various permeability models used with the new wicking model is also investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2010
Reza Masoodi - One of the best experts on this subject based on the ideXlab platform.
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darcy s law based numerical simulation for modeling 3d liquid absorption into porous wicks
Aiche Journal, 2011Co-Authors: Reza Masoodi, Hua Tan, Krishna M. PillaiAbstract:Liquid imbibition into polymer wicks, where a clear liquid front can be seen rising during the wicking process, is modeled using the concepts of flow in porous media. The flow of liquid behind the moving liquid front is modeled using the physics of single-phase flow in a porous medium where the Darcy’s law is combined with the continuity Equation and a capillary suction pressure is imposed at the liquid front. A novel numerical simulation PORE-FLOW V C based on the finite element/control volume method is proposed to model such imbibitional flows in wicks of complex shapes. A validation of the simulation is obtained by achieving an excellent comparison of its predictions with an experimental result, an analytical solution, and the Washburn Equation for the case of wicking against gravity in a cylindrical wick. The simulation is also used to predict a case of two-dimensional (2D) wicking in the altered cylindrical wicks with two different cross-sectional areas. Once again an excellent match is obtained with the experimental results, while analytical solutions for the single and double cross-section cases along with the Washburn Equation fail to predict the 2D wicking. Later, some other types of altered wicks with sharp changes in their cross-sectional areas were analyzed numerically for their wicking behavior. It was observed that the height of liquid front in a vertical wick as a function of time, which is proportional to the history of liquid imbibed, is strongly dependent on the extent of reduction in the wick cross-sectional area as well as its location vis-a `-vis the wick entrance. V C 2010 American Institute of Chemical Engineers AIChE J, 57: 1132–1143, 2011
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darcy s law based model for wicking in paper like swelling porous media
Aiche Journal, 2010Co-Authors: Reza Masoodi, Krishna M. PillaiAbstract:The wicking of liquid into a paper-like swelling porous medium made from cellulose and superabsorbent fibers was modeled using Darcy's law. The work is built on a previous study in which the Washburn Equation, modified to account for swelling, was used to predict wicking in a composite of cellulose and superabsorbent fibers. In a new wicking model proposed here, Darcy's law for flow in porous media is coupled with the mass conservation Equation containing an added sink or source term to account for matrix swelling and liquid absorption. The wicking-rate predicted by the new model compares well with the previous experimental data, as well as the modified Washburn Equation predictions. The effectiveness of various permeability models used with the new wicking model is also investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2010
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Darcy's law–based numerical simulation for modeling 3D liquid absorption into porous wicks
AIChE Journal, 2010Co-Authors: Reza Masoodi, Hua Tan, Krishna M. PillaiAbstract:Liquid imbibition into polymer wicks, where a clear liquid front can be seen rising during the wicking process, is modeled using the concepts of flow in porous media. The flow of liquid behind the moving liquid front is modeled using the physics of single-phase flow in a porous medium where the Darcy’s law is combined with the continuity Equation and a capillary suction pressure is imposed at the liquid front. A novel numerical simulation PORE-FLOW V C based on the finite element/control volume method is proposed to model such imbibitional flows in wicks of complex shapes. A validation of the simulation is obtained by achieving an excellent comparison of its predictions with an experimental result, an analytical solution, and the Washburn Equation for the case of wicking against gravity in a cylindrical wick. The simulation is also used to predict a case of two-dimensional (2D) wicking in the altered cylindrical wicks with two different cross-sectional areas. Once again an excellent match is obtained with the experimental results, while analytical solutions for the single and double cross-section cases along with the Washburn Equation fail to predict the 2D wicking. Later, some other types of altered wicks with sharp changes in their cross-sectional areas were analyzed numerically for their wicking behavior. It was observed that the height of liquid front in a vertical wick as a function of time, which is proportional to the history of liquid imbibed, is strongly dependent on the extent of reduction in the wick cross-sectional area as well as its location vis-a `-vis the wick entrance. V C 2010 American Institute of Chemical Engineers AIChE J, 57: 1132–1143, 2011
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Darcy's law‐based model for wicking in paper‐like swelling porous media
Aiche Journal, 2010Co-Authors: Reza Masoodi, Krishna M. PillaiAbstract:The wicking of liquid into a paper-like swelling porous medium made from cellulose and superabsorbent fibers was modeled using Darcy's law. The work is built on a previous study in which the Washburn Equation, modified to account for swelling, was used to predict wicking in a composite of cellulose and superabsorbent fibers. In a new wicking model proposed here, Darcy's law for flow in porous media is coupled with the mass conservation Equation containing an added sink or source term to account for matrix swelling and liquid absorption. The wicking-rate predicted by the new model compares well with the previous experimental data, as well as the modified Washburn Equation predictions. The effectiveness of various permeability models used with the new wicking model is also investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2010
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MODELING IMBIBITION OF LIQUIDS INTO RIGID AND SWELLING POROUS MEDIA
2010Co-Authors: Reza MasoodiAbstract:iii TABLE OF CONTENTS ix LIST OF FIGURES xvi LIST OF TABLES xxii NOMENCLATURE xxiv ACKNOWLEDGEMENTS xxviii Chapter 1: INTRODUCTION 1 1.1 Imbibition 1 1.2 Mathematical Modeling of Imbibition 1 1.2.1 The Darcy’s Law Based Approach 4 1.2.2 Washburn Equation 5 1.3 Capillary Pressure 6 1.4 Swelling Effects 8 1.5 Study of Special Cases 9 1.5.1 Darcy's Law-Based Model for Wicking in Polymer Wicks 9 1.5.2 A Washburn Equation Based Model for Wicking in Polymer Wicks 10 1.5.3 FEM Modeling of Wicking in Altered Polymer Wicks 11 1.5.4 Effect of External Pressure on Wicking into Paper Wipes 12
Wonjung Kim - One of the best experts on this subject based on the ideXlab platform.
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Dynamics of water imbibition through paper with swelling
Journal of Fluid Mechanics, 2020Co-Authors: Sooyoung Chang, Wonjung KimAbstract:We present a combined experimental and theoretical investigation of the dynamics of water imbibition through paper with swelling. The Washburn Equation has been widely used to describe the dynamics of the liquid absorption in paper, but its prediction of liquid imbibition speed has been reported to be inaccurate. Our recent study (Chang et al., J. Fluid Mech., vol. 845, 2018, pp. 36–50) demonstrated that the internal cavity of cellulose fibres composing the paper is partially responsible for the limited accuracy of the Washburn Equation based on oil imbibition experiments. Here we extend the investigation to water absorption through paper with swelling. We demonstrate that the swelling of the cellulose fibre network in addition to the internal voids of the cellulose fibres crucially affects the imbibition dynamics. Based on the microscopic observation that paper swelling is caused by the expansion of inter-fibre space, we suggest a mathematical model for water imbibition which considers both intra-fibre voids and swelling. By introducing parameters that characterize the swelling speed and volume of paper, our model markedly improves prediction of the water imbibition speed. The results provide not only a theoretical background for designing paper-based microfluidic systems, but also new insights into capillary flow through expandable porous media.
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Dynamics of liquid imbibition through paper with intra-fibre pores
Journal of Fluid Mechanics, 2018Co-Authors: Sooyoung Chang, Jaedeok Seo, Seokbin Hong, Duck-gyu Lee, Wonjung KimAbstract:We present a combined experimental and theoretical investigation of the dynamics of liquid imbibition through paper. The Washburn Equation is widely used to describe the dynamics of capillary flow through paper, but this classical model has limited accuracy, which often makes it difficult to use in developing analytic systems such as paper-based microfluidic devices. We here report that the internal cavity of the cellulose fibres composing paper is significantly responsible for the limited accuracy of the Washburn Equation. Our experiments demonstrated that liquid can be absorbed in the internal cavity of the cellulose fibres as well as in the inter-fibre pores formed by the fibre network. We developed a mathematical model for liquid imbibition by considering the flow through the intra-fibre pores based on experimental measurements of the intra-structure of cellulose fibres. The model markedly improves the prediction of the liquid absorption length, compared with the results of the Washburn Equation, thus revealing the physics behind the limits of the Washburn Equation. This study suggests that the accurate description of capillary imbibition through paper require parameters characterizing the internal pores of the cellulose fibres comprising the paper. Our results not only provide a new insight into porous media flows with different sized pores, but also provide a theoretical background for flow control in paper-based microfluidic systems.
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Dynamics of water imbibition through paper channels with wax boundaries
Microfluidics and Nanofluidics, 2015Co-Authors: Seokbin Hong, Wonjung KimAbstract:Although paper-based microfluidic devices have been of great interests because of their advantages in terms of manufacturing costs and simplicity, the dynamics of liquid imbibition through a porous medium has not entirely been understood. Washburn Equation describes liquid imbibition with respect to time through a one-dimensional porous medium, but it has recently been reported that Washburn Equation is not valid for paper channels with wax boundaries. Here, we present the results of a combined experimental and theoretical investigation of water imbibition through paper channels with wax boundaries. We propose a model that explains how hydrophobic channel boundaries affect the imbibition dynamics in the channels. The model was tested by comparing experimental results for paper channels with various forms of boundaries. Our results suggest simple ways to control the flow speeds in paper-based devices through the design of the hydrophobic boundaries.
Kenneth Stuart Sorbie - One of the best experts on this subject based on the ideXlab platform.
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the extended Washburn Equation and its application to the oil water pore doublet problem
Journal of Colloid and Interface Science, 1995Co-Authors: Kenneth Stuart Sorbie, Steven Robert McdougallAbstract:Abstract The Equations of capillary rise or wetting-phase imbibition into a cylindrical capillary are frequently described by the Washburn Equation. From this starting point, the familiar pore doublet model for imbibition into a wide/narrow pair of pores has been developed. This simple analytically soluble model can afford insights into the physics of immiscible water/oil displacements in porous media, which are of importance to waterflooding of oil reservoirs. Here, we reexamine the basis of both the Washburn Equation and the formulation of the pore doublet model by incorporating a more rigorous treatment of the fluid mechanics. We have extended Equations previously proposed by Szekely et al. to describe water/off displacement in a capillary and it transpires that certain additional inertial terms, which appear in the full formulation of the capillary displacement problem, may be particularly important at the pore size and aspect ratio commonly encountered within porous media. The main result of this additional physics is that the pore filling time and the relative filling order of large and small pores may change since these quantities depend on the pore aspect ratio in the extended formulation. When this fuller formulation is embedded within the extended pore doublet model, we find that the modified Equations lead to different findings for certain cases, compared with previous well-known (analytical) solutions. The original pore doublet model is fully characterised by three quantities, the aspect ratio, r 2 / L , the ratio of capillary radii, r 1 / r 2 , and the fluid "supply," i.e., free supply or restricted supply, which is characterized by a velocity, V 0 2 . In the extended pore doublet model there is a fourth governing quantity, the pore scale Reynolds number, N Re , which describes the inertial terms in the extended Washburn Equation. The resulting coupled differential Equations for the extended pore doublet model do not admit an analytical solution and must be solved numerically. Under certain conditions of very restricted supply of wetting fluid (low V 0 2 ), the extended model agrees very closely with the conventional pore doublet results. However, there are cases which are common at the pore scale (and pore aspect ratio) where significant differences are seen. The relevance of these findings to the modeling of imbibition processes within network models of porous media is discussed.
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The Extended Washburn Equation and Its Application to the Oil/Water Pore Doublet Problem
Journal of Colloid and Interface Science, 1995Co-Authors: Kenneth Stuart Sorbie, Steven Robert McdougallAbstract:Abstract The Equations of capillary rise or wetting-phase imbibition into a cylindrical capillary are frequently described by the Washburn Equation. From this starting point, the familiar pore doublet model for imbibition into a wide/narrow pair of pores has been developed. This simple analytically soluble model can afford insights into the physics of immiscible water/oil displacements in porous media, which are of importance to waterflooding of oil reservoirs. Here, we reexamine the basis of both the Washburn Equation and the formulation of the pore doublet model by incorporating a more rigorous treatment of the fluid mechanics. We have extended Equations previously proposed by Szekely et al. to describe water/off displacement in a capillary and it transpires that certain additional inertial terms, which appear in the full formulation of the capillary displacement problem, may be particularly important at the pore size and aspect ratio commonly encountered within porous media. The main result of this additional physics is that the pore filling time and the relative filling order of large and small pores may change since these quantities depend on the pore aspect ratio in the extended formulation. When this fuller formulation is embedded within the extended pore doublet model, we find that the modified Equations lead to different findings for certain cases, compared with previous well-known (analytical) solutions. The original pore doublet model is fully characterised by three quantities, the aspect ratio, r 2 / L , the ratio of capillary radii, r 1 / r 2 , and the fluid "supply," i.e., free supply or restricted supply, which is characterized by a velocity, V 0 2 . In the extended pore doublet model there is a fourth governing quantity, the pore scale Reynolds number, N Re , which describes the inertial terms in the extended Washburn Equation. The resulting coupled differential Equations for the extended pore doublet model do not admit an analytical solution and must be solved numerically. Under certain conditions of very restricted supply of wetting fluid (low V 0 2 ), the extended model agrees very closely with the conventional pore doublet results. However, there are cases which are common at the pore scale (and pore aspect ratio) where significant differences are seen. The relevance of these findings to the modeling of imbibition processes within network models of porous media is discussed.
